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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 1872s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1872.q3 | 1872s1 | \([0, 0, 0, 69, 362]\) | \(12167/26\) | \(-77635584\) | \([]\) | \(480\) | \(0.19823\) | \(\Gamma_0(N)\)-optimal |
| 1872.q2 | 1872s2 | \([0, 0, 0, -651, -12742]\) | \(-10218313/17576\) | \(-52481654784\) | \([]\) | \(1440\) | \(0.74753\) | |
| 1872.q1 | 1872s3 | \([0, 0, 0, -66171, -6551638]\) | \(-10730978619193/6656\) | \(-19874709504\) | \([]\) | \(4320\) | \(1.2968\) |
Rank
sage: E.rank()
The elliptic curves in class 1872s have rank \(0\).
Complex multiplication
The elliptic curves in class 1872s do not have complex multiplication.Modular form 1872.2.a.s
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
